Natasha's income is $300 per month. She spends all of it on tickets to concerts and films. A concert ticket costs $15 and a fi lm ticket costs $10. Her marginal rate of substitution for concerts with films, MRSCF , is F/C, where C stands for the number of concert tickets and F stands for the number of films. Fractions are allowed-for example, if she buys half of a concert ticket, that means she goes to a concert every other month). How many film tickets will she purchase, and how many concert tickets?
The Solution Notice that MRSCF decreases as C rises and F falls. Therefore, each of Natasha's indifference curves has a declining MRS. To find a best choice, we look for a bundle on her budget line that satisfies the tangency condition.
At Natasha's best choice, her marginal rate of substitution between films and concerts equals the price ratio: MRSCF _ PC/PF . Substituting the information contained in the statement of the problem gives us the following: F/C _ 15/10 _ 1.5. In other words, Natasha purchases 1.5 times as many movie tickets as concert tickets.
The formula for Natasha's budget line is PCC _ PFF _ 300. Substituting the values of the prices into this formula, we have 15C _ 10F _ 300. Using the fact that F _ 1.5C gives us 15C _ 10(1.5C) _ 300, or 30C _ 300. So C _ 10, and F _ 15.
Natasha purchases 10 concert tickets and 15 movie tickets.